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Commensurations and metric properties of houghton’s groups

Burillo, José
; 
Cleary, Sean
; 
Martino, Armando
; 
Röver, Claas
Repository DOI
Publication Date
2016-11-21
Keywords
houghton's groups, commensurations
Type
Article
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Citation
Burillo, José; Cleary, Sean; Martino, Armando; Röver, Claas (2016). Commensurations and metric properties of houghton’s groups. Pacific Journal of Mathematics 285 (2), 289-301
Abstract
We describe the automorphism groups and the abstract commensurators of Houghton's groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays.
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Publisher
Mathematical Sciences Publishers
Publisher DOI
10.2140/pjm.2016.285.289
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)